Geometry of the parallelism in polar spine spaces and their line reducts

Krzysztof Petelczyc, Krzysztof Prażmowski, Mariusz Żynel

Abstract


The concept of spine geometry over a polar Grassmann space was introduced in [9]. The geometry in question belongs also to a wide family of partial affine line spaces. It is known that such a geometry -- e.g. the ``ordinary'' spine geometry, as considered in [13, 14] can be developed in terms of points, so called affine lines, and their parallelism (in this case this parallelism is not intrinsically definable: it is not `Veblenian', cf. [11]). This paper aims to prove an analogous result for polar spine spaces. As a by-product we  obtain several other results on primitive notions for the geometry of polar spine spaces.

Keywords


Grassmann space, projective space, polar space, spine space, coplanarity, pencil of lines

Full Text:

MANUSCRIPT


DOI: https://doi.org/10.26493/1855-3974.2201.b65

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications